A quadratic function is a parabola of the form:
y-k=a(x-h)² where (h,k) is the vertex.
We know the vertex so h=-3 and k=-1, therefore:
y+1=a(x+3)².
And we know the parabola passes through (0,8) so:
8+1=a(0+3)²=9a, so 9a=9 and a=1.
The equation is y+1=(x+3)²=x²+6x+9,
y=x²+6x+9-1=x²+6x+8.